An early vote tally released in the afternoon should give an indication of how the candidates have performed although official results will not be announced until mid-March, and the vote is likely to go to an April run-off.
Basuki Tjahaja Purnama shows his ink-stained finger after casting his vote on Wednesday.
"There has been a long decline of religious freedom in Indonesia", he said, adding that religion had been exploited in the run up to Wednesday's election.
Supporters of Basuki "Ahok" Tjahaja Purnama, Jakarta governor and his running mate Djarot Saiful Hidayat cheer during a campaign rally in Jakarta, Indonesia, 11 February 2017.
Baswedan is an academician and former minister of education in the government of President Joko "Jokowi" Widodo. Popular with middle-class residents for his efforts against corruption and to improve the quality of life, accusations against him of blasphemy - a criminal offense - surfaced in September and he is now on trial. Basuki, who was raised by Muslim adoptive parents, has explained to the jury that his joke was meant to urge low information voters not to be deceived by Muslims using the verse to deter people from electing a non-Muslim leader.
Purnama has won middle-class support for cutting red tape and improving the performance of the bureaucracy, but he has been campaigning for re-election while on trial for blasphemy, after being accused of insulting the Koran. If convicted of blasphemy, he faces up to five years in prison.
As results came in he told his supporters, many wearing his signature checked shirt, that it was "not over yet".
His party said he had listened to the concerns of voters, including people evicted during Mr Purnama's operations to clean-up slum areas, Reuters reports.
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Clearly, this had upset many people in the United States, and even those who are trying to escape from danger in another country. Ben Sasse (R-Neb.) said "I don't understand language like that, we don't have any so-called judges, we have real judges".
Some analysts view today's election as a test of religious and cultural pluralism in the world's largest Muslim country and Southeast Asia's largest economy. About 85% of the population are Muslim, but the country officially respects six religions.
The elections are seen as a prelude to the Indonesian general election in 2020.
Most observers are warning that any run-off between Governor Purnama and Anis Baswedan could inflame religious tensions further.
With quick-count results suggesting he is out of the race, Jakarta gubernatorial candidate Agus Harimurti Yudhoyono conceded defeat in the three-horse race for the capital's top post on Wednesday (Feb 15) evening.
"In an election campaign you need to bring everyone together and reach out to all groups".
Office worker Emma Kusuma, who was browsing through the merchandise this week, said she had made the trip from the outskirts of Jakarta. "He is one who started this".
Agus and Anies, who were once seen as moderate Muslim figures, have been hoping to win support from hard-liners.